The constant modulus algorithm (CMA) updates its weight vector to minimize the modulus variation of the output signal. In this paper, the convergence behavior of the CMA used in interference cancellation application is studied. We first investigate the optimum weight vector that minimizes the performance index of the CMA which is defined as the mean-squared difference between the estimated and true moduli. We then analyze the convergence behavior of the squared output modulus and the performance index. Based on these analysis results, several convergence properties of the CMA are discussed.